On Tue, Jan 1, 2019 at 7:09 PM Brent Meeker <[email protected]> wrote:
* > And for two spacelike events (as I specified) h^2 < 0 so you have made > the interval along a world line, the proper time, imaginary. * > The spacetime distance d is *not* the proper time, the spacetime distance is an invariant, it's the same for all observers, but proper time is *not* invariant; your proper time is not my proper time if we're moving relative to each other, accelerating at different rates, or in different gravitational fields. But we both always agree on how much we moved through spacetime since our last meeting. But obviously if d^2 = r^2 - (ct)^2 (where d is the invariant distance in spacetime and r the distance in space) then d can be imaginary if t is large, and that's one reason physicists usually use d^2 not d when they want a invariant. If it's your position that the formula given in all books on relativity for that spacetime invariant are wrong then please inform us of the correct one. If the formula is correct then the distance through spacetime simply can *not* be the proper time as you said. > > *You're making a big distinction between spacelike 'distance' and > 'proper time'. But it's just muddling the point that the geodesic followed > by a body is the longest interval. * > Yes a clock following a geodesic will show the largest proper time and yes I am making a big deal about the proper time not being the spacetime distance because they're not even in compatible units, one is in seconds and the other is in meters. It's like trying to subtract acres from nanoseconds, it doesn't make any physical sense. > >>You can never find a distance between anything by subtracting seconds >> from meters, that would be gibberish, but you can subtract meters from >> meters. > > *>That's why the speed of light is now just a conversion factor.* > Just? The speed of light is *just* the bridge between two otherwise incompatible quantities because you *just* can't subtract seconds from meters! And it's *just* a fact that Google was right and you were wrong when it said a geodesic was *"the shortest possible line between two points on a sphere or other curved surface".* >>Doesn't slow a clock down relative to what? > > > * > It's a negative, John! It doesn't slow down realtive to anything. * > Of course it does! If 2 clocks start out synchronized on the Earth and one stays put but the other is put on a rocket and blasted away into space at near the speed of light and then accelerated in the opposite direction so it can return to Earth then the clocks will no longer be synchronized when they meet again. So obviously *one clock must have slowed down relative to the other, *or equivalently one clock must have sped up relative to the other because that's what "unsynchronized" means. > * > Ideal clocks in relativity are assumed to accurately measure proper > time along their world line. * > And that's why I said "in Relativity, a clock never slows down relative to an observer in the same reference frame" > > *They never run slow or fast...they just follow different paths.* > But that's exactly what clocks slowing down or speeding up between events means, following different paths through spacetime. > > *You're one that referred to the clock being slowed down. "Then one > twin would encounter a intense gravitational field that the other twin did > not and gravity will slow down a clock just like moving fast will."* > Yes and in that I was absolutely correct. When the clocks meet again after one went on its rocket journey the previously synchronized clocks are now un synchronized. Unsynchronized means showing different times, so during the journey one clock *MUST* have run slower than the other. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
